The double-beta decay of Zr-96 to the ground and excited states of the
daughter nucleus Mo-96 is sought with both plastic and NaI scintillat
ors in combination with proportional chambers. A new limit on the beta
beta 0 nu mechanism with m(nu) not equal 0 is obtained by using only
5.5 g of Zr-96 for the measurement time of 2570 h. For the pp decay of
Zr-96 to excited states, our present results are comparable with the
best results reported recently. The sensitivity of the experiment to t
he beta beta 2 nu decay of Zr-96 is estimated.